Asymptotic theory for estimating the parameters of a Lévy process |
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Authors: | Michael G Akritas |
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Institution: | (1) Massachusetts Institute of Technology, Mssachusetts, USA |
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Abstract: | Summary We consider consistency and asymptotic normality of maximum likelihood estimators (MLE) for parameters of a Lévy process of
the discontinuous type. The MLE are based on a single realization of the process on a given interval 0,t]. Depending on properties of the Lévy measure we either consider the MLE corresponding to jumps of size greater than ε and,
keepingt fixed, we let ε tend to 0, or we consider the MLE corresponding to the complete information of the realization of the process
on 0,t] and lett tend to ∞. The results of this paper improve in both generality and rigor previous asymptotic estimation results for such
processes. |
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Keywords: | |
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